Answer:
Absolute maximum at (3,0)
Absolute minimum at (1,1)
Step-by-step explanation:
Given - f(x, y) = x⁴ + y⁴ − 4xy + 2, D = {(x, y) | 0 ≤ x ≤ 3, 0 ≤ y ≤ 2}
To find - Find the absolute maximum and minimum values of f on the set D.
Proof -
Given that, f(x, y) = x⁴ + y⁴ − 4xy + 2
Now,
Differentiate f(x,y) with respect to x and y , we get
[tex]f_{x}(x,y)[/tex] = 4x³ - 4y
[tex]f_{y}(x,y)[/tex] = 4y³ - 4x
Now,
For the critical point, put [tex]f_{x}(x,y)[/tex] , [tex]f_{y}(x,y)[/tex] = 0
we get
4x³ - 4x = 0
⇒x = 0, -1, 1
but given the range of x is 0 ≤x ≤ 3
⇒x = 0, 1
⇒y = 0, 1
∴ we get
2 critical points (x,y) = (0,0) , (1,1)
Now,
Put the values of x and y in f(x,y), we get
f(0,0) = 0 + 0 - 0 + 2 = 2
f(1,1) = 1 + 1 - 4 + 2 = 0
Now,
for the max and min values, finding the critical value is not enought, we have to find the values in the domain also.
Given domain is 0 ≤ x ≤ 3, 0 ≤ y ≤ 2
So, we have to check the values at the rectangle that have the coordinates
(0,0), (0,2), (3,2), (3,0)
Now,
f(0,0) = 0 + 0 - 0 + 2 = 2
f(0,2) = 0 + 16 - 0 + 2 = 18
f(3,2) = 81 + 16 - 24 + 2 = 75
f(3,0) = 81 + 0 - 0 + 2 = 83
∴ we get
Absolute maximum at (3,0)
Absolute minimum at (1,1)
Help please I’ll give extra points
Answer:
The perimeter of the resulting image is 13 centimeters
Step-by-step explanation:
we know that
Rotation, reflection, and translation are transformations that do not produce changes in the dimensions of the figure, while dilation is a transformation that does affect the dimensions of the figure.
In this problem, we have rotation and reflection
therefore
The perimeter of the resulting figure is the same as the original figure
According to the Central Limit Theorem, which statements(s) are TRUE. There may be more than 1 correct answer. A. An increase in sample size from n = 16 to n = 25 will produce a sampling distribution for the sample means that has a smaller standard deviation. B. The larger the sample size, the more the sampling distribution of sample means will resemble a normal distribution C. The mean of the sampling distribution of sample means for samples of size n = 15 will be the same as the mean of the sampling distribution for samples of size n = 100. D. The mean of a sampling distribution of sample means is equal to the population mean divided by the square root of the sample size. E. The larger the sample size, the more the sampling distribution of sample means resembles the shape of the population.
Answer:
Options A, B and C are correct.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
From the Central Limit Theorem, we have that:
The larger the sample size, the closer to the normal distribution the distribution of sample means is.
No matter the sample size, the mean is the same.
The larger the sample size, the smaller the standard deviation.
The smaller the sample size, the larger the standard deviation.
So the correct options are:
A, B, C
100 times 5 dino nuggie is how much
Answer:
500 dino nuggies.
Step-by-step explanation:
Hope this helps
Answer:
500 dino nuggies!!!
Step-by-step explanation:
What is 4.9 subtract 0.6
Answer: 4.3
Step-by-step explanation:
4.9-.6=4.3
Write an equation to represent the following description. Seventeen more than eight times a number is −6.
Can someone help me with this its preatty easy
Answer:
31,400
Step-by-step explanation:
Hope this helps and have a wonderful day!!!
WILL GIVE BRAINLIEST!!!!!
Answer:
6
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
One half of a number , n is at most 24
Answer:
So if N is 24, then the number is 12.
Step-by-step explanation:
24 / 2 = 12
1) A store sells small and large TV sets in the ratio 2:3. The total stock is 70
sets.1) How many small and large sets are in stock? 2)If the number of large
sets is increased by 8,what is the new ratio of small to big*
Answer:
(a)
[tex]Small = 28[/tex]
[tex]Large = 42[/tex]
(b)
[tex]Ratio = 14 : 25[/tex]
Step-by-step explanation:
Given
[tex]L = Large\\ S = Small[/tex]
[tex]S : L = 2 : 3[/tex]
[tex]Total = 70[/tex]
Solving (a): Number of each set.
The small set is calculated as:
[tex]Small = \frac{S}{S + T} * Total[/tex]
[tex]Small = \frac{2}{2+3} * 70[/tex]
[tex]Small = \frac{2}{5} * 70[/tex]
[tex]Small = 0.4 * 70[/tex]
[tex]Small = 28[/tex]
Using complement rule.
[tex]Large = Total - Small[/tex]
[tex]Large = 70 - 28[/tex]
[tex]Large = 42[/tex]
Solving (b): Increase large by 8.
The ratio is then calculated as:
[tex]Ratio = Small : Large + 8[/tex]
[tex]Ratio = 28 : 42 + 8[/tex]
[tex]Ratio = 28 : 50[/tex]
Divide by 2
[tex]Ratio = 14 : 25[/tex]
Real word example where a
piecework function might be used
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Explanation:
Garment factory: workers may get paid by the number of pieces they complete.
__
Wood chopping: the worker gets paid by the number of cords of wood they produce, not by how long it takes.
__
Haircut -- the cost is the same (for the same type haircut) even if more time is spent
____
The above are instances where an individual worker gets paid by the piece they produce. There are numerous instances of companies getting paid by the job, regardless of the length of time or the quantity of materials required to do the job.
Lawn mowing -- the price is fixed each time the crew mows the lawn
Oil Change -- the cost of changing the oil in the car is not dependent on the time it takes or the amount of oil used
Car wash -- a fixed price is paid each time (at an automatic car wash)
Find the sum of -3x^2-4x+3−3x 2−4x+3 and 2x^2-x+32x 2 −x+3.
Answer:
28x^2-10x+9
Step-by-step explanation:
28x^2-10x+9
Consider the following statement. ∀a ∈ Z, (a − 1) a is not an integer. (a) Select the correct negation for this statement. For every integer a, a − 1 a is an integer. There is an integer a such that a − 1 a is not an integer. For every integer a, a − 1 a is not an integer. There is an integer a such that a − 1 a is an integer. (b) Is the given statement true or false? If the statement is true, enter TRUE; if the statement is false, enter a value of a that could be used as part of a counterexample that justifies its falseness.
Answer:
a) There is an integer a such that [tex]\frac{a-1}{a}[/tex] is an integer
b) False
Step-by-step explanation:
Statement : ∀a ∈ Z, (a − 1) a is not an integer
A) The correct negation will be :
There is an integer a such that [tex]\frac{a-1}{a}[/tex] is an integer
B) The Given statement is FALSE because
when we assume the value of a = 1
( a - 1 ) / a = (1 - 1 ) / 1 = 0 ; which is an integer
I’ll give points + brainslist, if you don’t know don’t bother answering (:
HURRY! What is the circumference of the circle below? Use 3.14 for π.
Answer:
2.14 divided by 5 x 2 is the ansewer
Step-by-step explanation:
Help me I need to get this right
Answer:
0.006 (decimal form) or 0.6% (percentage form)
Step-by-step explanation:
0.1(0.2)(0.3) = 0.006
The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results? What is the estimate of the mean proportion of failures for these instructors?
INSTRUCTOR NUMBER OF FAILURES
Prof. A 13
Prof. B 0
Prof. C 11
Prof. D 16
Answer:
D. 16
Step-by-step explanation:
A quality analyst wants to construct a control chart for determining whether three machines, all producing the same product, are under control with regard to a particular quality variable. Accordingly, he sampled four units of output from each machine, with the following results:
MACHINE MEASUREMENTS
#1 17 15 15 17
#2 16 25 18 25
#3 23 24 23 22
In Exercises 1-4, the sample size n, probability of success p, and probability of
failure q are given for a binomial experiment. Determine whether you can use a
normal distribution to approximate the distribution of x.
1. n = 24, p = 0.85, 9 = 0.15
2. n = 15, p = 0.70, q = 0.30
3. n = 18, p = 0.90, q = 0.10
4. n = 20, p = 0.65, q = 0.35
Answer:
1. No
2. No
3. No
4. Yes
Step-by-step explanation:
Binomial approximation to normal.
The binomial probability distribution has parameters n, p and q.
If
[tex]np \geq 5[/tex] and [tex]nq \geq 5[/tex], you can use the normal approximation.
1. n = 24, p = 0.85, q = 0.15
[tex]np = 24*0.85 = 20.4 > 5[/tex]
[tex]nq = 24*0.15 = 3.6 < 5[/tex]
So no.
2. n = 15, p = 0.70, q = 0.30
[tex]np = 15*0.7 = 10.5 > 5[/tex]
[tex]nq = 15*0.3 = 4.5 < 5[/tex]
So no.
3. n = 18, p = 0.90, q = 0.10
[tex]np = 18*0.9 = 16.2 > 5[/tex]
[tex]nq = 18*0.1 = 1.8 < 5[/tex]
No
4. n = 20, p = 0.65, q = 0.35
[tex]np = 20*0.65 = 13 > 5[/tex]
[tex]nq = 20*0.35 = 7 > 5[/tex]
Yes
PLS HELP
Rusty has a cap collection. He has 5 shelves with 7 football team caps on each shelf. He has 3 shelves with 13 baseball caps on each shelf. He gives his best friend 5 football caps and 2 baseball caps.
How many caps, c, does Rusty have now?
Rusty has a total of ___ caps.
Answer:
19
Step-by-step explanation:
Determine whether the equation represents direct, joint, or inverse variation. Then identify the constant.
t = 100/s
y/5 = x
p/qr = 4
C = 2πr
V = 1/3πr^2h
xy = 2/5
Solve using the substitution method:
6x + y =15
4x + 3y = 31
Answer:
the answers to this are x= 1 and y= 9
The amount of water that fits in a fish tank represents the _______________ of the fish tank.
Answer:
Volume
Step-by-step explanation:
The amount of water that fits in a fish tank represents the Volume of the fish tank.
When you pour water, it occupies the space and the weight of the tank increases. So, it represent the volume
the answer is report you welcome
Answer:
report
Step-by-step explanation:
Answer:
Step-by-step explanation:
Report???? What
Hey y’all answers in the picture ABC or D. Plz help
Answer:
D
Step-by-step explanation:
Lets use the the chart. The (5,9) if the 5 was doubled that it would equal to 10. Now you subract 1 from it making it 9.
Which is the function g(x) for a restricted domain?
O g(x) = 3x-4; 2-4
O g(x) = 3x + 4; x > 0
O g(x) = 3/x+4; x 24
O g(x) = 35-4;> 0
The answer choice which correctly describe s the function g (x) for a restricted domain as required to be determined in the task content is; g (x) = ³√(x + 4) , x ≥ -4.
Which function correctly represents the function g (x) for a restricted domain?As evident in the task content, the function which correctly represents the function g (x) for a restricted domain is to be identified.
By observation of the function;
g (x) = ³√(x + 4) , x ≥ -4.
As evident in the task content; the lowest value of g(x) is; 0.
By checking; when x = -4; the corresponding value of g (x) is;
g (-4) = ³√(-4 + 4)
g (-4) = 0.
On this note, the required function is; g (x) = ³√(x + 4) , x ≥ -4.
Read more on functions and domain;
https://brainly.com/question/20253960
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Mr. Thorbes bought a new journal for his poetry. If the journal normally cost $22 but was on sale for 20% off, how much did Mr. Thorbes save?
Answer:
He would save $4.40
Step-by-step explanation:
And in total he would pay 17.60
Three more than four times the difference of x and 2 is 36
Answer:
3+4 (x - 2) =36 x= 10.25
Step-by-step explanation:
Rectangles R and S are similar. If the area of rectangle R is 40, what is the area of rectangle S?
Answer:
14.4 units²
Step-by-step explanation:
The ratio of Area of rectangle R to area of rectangle S = square of the length of rectangle R to square of lthe ength of rectangle S
Let the area of rectangle S be represented by x, therefore:
40 : x = 8² : 4.8²
40/x = 64/23.04
Cross multiply
x*64 = 40*23.04
64x = 921.6
x = 921.6/64
x = 14.4
Area of rectangle S = 14.4 units²
What are the polar coordinates of the rectangular coordinates (2, -2√3)?
A. (4, 11π/6)
B. (4, 5π/3)
C. (2, 5π/3)
D. (2, 11π/6)
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Answer:
B. (4, 5π/3)
Step-by-step explanation:
If you sketch the location of the point, you find the coordinates correspond to the side lengths of a 30°-60°-90° "special" triangle. The reference angle is 60°, or π/3 radians, and the magnitude of the vector is twice the short dimension, so is 2×2 = 4.
The polar coordinates are (4, 5π/3).
please help will give brainliest!
Answer:
1. x = 14
2. c = 12
3. d = 4
4. w = 8
5. z = 54
6. d = 20
7. n = 26.4
8. k = 15
Step-by-step explanation:
The total length of a road trip was 15.6 hours. If highway signs are posted every 0.06 hours, including one at the end of the road trip, how many highway signs will there be on the road trip?
Answer:
The answer is 260.
Step-by-step explanation:
15.6/.06=260.